Question

Q1. The sum of the numerator and denominator of fraction is 3 less than twice the denominator. If the
numerator and denominator both are decreased by 1, the numerator becomes half the
denominator.
Q2. Amar gives Rs. 9000 to some athletes of a school as scholarship every month. Had there been 20
more athletes each would have got Rs. 160 less. Form a pair of linear equations for this and find
the no. of athletes.
Q3. Find the value of k so that the equations x + 2y = – 7, 2x + ky + 14 = 0 will represent coincident
lines.
Q 4. Give linear equations which is coincident with 2 x + 3y - 4 = 0
Q5. What is the value of a for which (3, a) lies on 2x – 3y = 5
Q6. The sum of two natural nos. is 25 of their difference is 7. Find the nos.
Q7. Dinesh in walking along the line joining (1, 4) and (0, 6), Naresh is walking along the line joining
(3, 4,) and (1,0). Represent on graph and find the point where both of them cross each other.
Q8. Solve the pair or linear equations x – y = 2 and x + y = 2. Also find p if p = 2x + 3
Q9. For what value of K the following system of equation are parallel. 2x + Ky = 10; 3x + (k + 3) y = 12
Q10. Form a pair of linear equations for the following situation assuming speed of boat in still water as ‘x’
and speed of stream ‘y’ : A boat covers 32 km upstream and 36 km downstream in 7 hours,It also
covers 40 km upstream and 48 km downstream in 9 hours. Also find the values of x and y.
Q11. Check graphically whether the pair of linear equations 3x + 5y = 15, x – y = 5 is consistent. Also
check whether the pair is dependent.

Answer 1

Let the fraction be x/y.

As per given information,
(i)
x+y = 2y - 3

x - y = - 3................(1)

(ii)
x-1 /y -1 = 1/2

2x - 2 = y -1

2x - y = 1.................(2)

(2) - (1)

x = 4

y = x+3 = 7

The required fraction is 4/7

I hope this answer helps you

Answer 2

Q6.

In the attachment I have answered this problem.

As per the given information
equations are formed.

They have solved by elimination method .

See the attachment for detailed solution.